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Determination of the characteristic parameters in the special collinear space in the general case
Author(s) -
Sonja Krasić,
Miroslav Markovič
Publication year - 2007
Publication title -
facta universitatis - series architecture and civil engineering
Language(s) - English
Resource type - Journals
eISSN - 2406-0860
pISSN - 0354-4605
DOI - 10.2298/fuace0701049k
Subject(s) - quadrangle , mathematics , projective plane , projective space , geometry , space (punctuation) , point (geometry) , plane (geometry) , projective geometry , pencil (optics) , real projective plane , cross ratio , pure mathematics , constructive , mathematical analysis , algebraic geometry , collineation , projective test , physics , optics , computer science , archaeology , process (computing) , correlation , history , operating system
The projective space consists of the finitely and infinitely distant elements. The special collinear spaces in the general case, are set with five pairs of biunivocally associated points, so the quadrangle in the first space obtained by the three principal and one penetration point of the remaining two through the plane of the first three identical or similar to the associated quadrangle obtained in the same way in the second space. In order to associate two special collinear spaces, it is necessary to determine the following characteristic parameters: vanishing planes, space axes (principal normal lines), foci (apexes of the associated identical bundles of straight lines) and directrix plane (associated identical fields of points). The paper is based on constructive processing of the special collinear spaces in the general case. The structural methods which are used are Descriptive Geometry (a pair of Mange's projections) and Projective geometry

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